Question 1015407
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Solve for x
log(base 4) x + log(base 4) (x-2) = 1
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It is equivalent to

x*(x-2) = 4,     (1)

{{{x^2 -2x -4}}} = {{{0}}},

{{{x[1,2]}}} = {{{(2 +- sqrt(4 +4*4))/2}}} = {{{2 +- sqrt(20))/2}}} = {{{1 +- sqrt(5)}}}.

So, the solutions of the equation (1) are {{{1+sqrt(5)}}} and {{{1-sqrt(5)}}}.

Only positive value x = {{{1 + sqrt(5)}}} satisfies the original equation.
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